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Understanding error patterns in students' solutions to linear function problems to design learning interventions

learning AND INSTRUCTION 2024年 92卷

作者： Elagha, Noor Pellegrino, James W. Univ Illinois Dept Psychol Chicago IL 60607 USA

Background: Reasoning with and about linear functions (LF) is considered essential knowledge for college readiness, but evidence shows that students experience difficulty in this topic. There were two overarching aims of the reported studies. One was to assess students ' understanding of LF and discern the cognitive underpinnings of common errors they make in these types of problems. The second was to explore designs of a learning intervention that can ameliorate these misunderstandings. Methods: In Study 1, analyses of performance on Verbal Description, Table, and Graph LF problem types showed substantial and interpretable errors on the latter two. errors reflected systematic conceptual and procedural misunderstandings associated with interpretation of structural features of Table and Graph LF problems. The results for LF Table and Graph problems suggested that students could benefit from error focused interventions. In Study 2, information about common errors from Study 1 was used to inform the design of instructional interventions using three worked example conditions: (1) error detection and correction, (2) error correction only, and (3) no error (control). Results & conclusions: Results of quantitative and qualitative analyses showed enhanced performance in all intervention conditions and across both problem types and were particularly impactful for both problem types when error correction was required in worked examples. Findings from both studies are discussed in terms of implications for learning environments, including initial instruction and diagnostic assessment.

关键词： Mathematical knowledge Error patterns Problem solving Worked examples learning from errors Math learning and instruction

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learning from Self-Diagnosis Activities when Contrasting Students' Own Solutions with Worked Examples: the Case of 10th Graders Studying Geometric Optics

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RESEARCH IN SCIENCE EDUCATION 2021年第2期51卷 523-546页

作者： Safadi, Rafi' Saadi, Sheren Acad Arab Coll Educ Israel Dept Sci Educ 22 Hahashmal StPOB 8349 IL-33145 Haifa Israel Comprehens Sch C Shefaamre Tawfeq Ziad StPOB 780 IL-20200 Shefaamre Israel

Self-diagnosis activities require students to self-diagnose their solutions to problems they solved on their own by detecting and explaining their errors. Worked examples, a step-by-step demonstration of how to solve a problem, are often used to support students in self-diagnosis activities. However, studies indicate that students often fail to exploit worked examples in traditional self-diagnosis activities when simply required to self-diagnose their solutions. This study analyzes a new self-diagnosis activity developed by the first author to prompt students to effectively use worked examples when self-diagnosing: the written worked examples only constitute one part of a scoring rubric and the students are required to both self-diagnose their solutions and then self-score them. This activity was hypothesized to encourage students to exploit the worked examples more thoroughly, and by extension detect and learn from their errors to a greater extent than students administered the traditional self-diagnosis activities. Six 10th grade advanced physics classes completed a pre-test/intervention/post-test after finishing a unit in geometric optics. Students in each class were randomly assigned to the new self-diagnosis activity (83 students) or the traditional self-diagnosing activity (79 students). Students assigned the new activity detected and learned more from their errors than students administered the traditional activity. It is argued that more in-depth error detection contributed overall to students' learning by triggering a series of implicit steps that prompted them to self-regulate their cognitions in a way that provided opportunities to self-repair their naive concepts.

关键词： Erroneous solutions Geometric optics learning from errors Self-assessment Self-diagnosis Worked examples

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learning from troubleshooting activities when contrasting erroneous examples with worked examples in the physics classroom

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Physics Education 2020年第5期55卷 1-11页

作者： Safadi, Rafi' Ababsy, Ranin Science Education Department Academic Arab College for Education in Israel - Haifa 22 Hahashmal St. Haifa 33145 Israel

Research indicates that troubleshooting activities that require students to reflect on pre-prepared erroneous examples, i.e. erroneous solutions to problems that correspond to common naïve ideas, impact their learning positively. These include asking students to diagnose erroneous examples;in other words, detect the conceptual errors and then explain why these errors are wrong. One of the major challenges is to determine the best ways to support student learning with troubleshooting activities. One suggestion involves contrasting erroneous examples with worked examples through a step-by-step demonstration of how to solve a problem. Here, a new troubleshooting activity designed to prompt students to learn more effectively from erroneous examples is described and assessed. The worked examples only constitute one part of the rubric, and students are required to both diagnose erroneous examples and then score them. Six 8th grade classes from three schools (two classes each from a different school taught by the same teacher) completed a pre-test/intervention/post-test after finishing a unit in simple electric circuits. In the intervention, in each school, one class was randomly assigned to the new activity (45 students) and the other class to the traditional troubleshooting activity with worked examples without rubrics (46 students). The findings suggest that the new activity enabled more students to learn from the erroneous examples than the traditional activity, regardless of whether the students' naïve ideas resembled the ones committed in the erroneous examples, and confirm the effectiveness of the new activity in 8th graders studying simple electric circuits. In a companion study by the first author (under review), the findings confirmed the effectiveness of the new activity in 10th graders studying geometric optics. Taken together, the findings of both studies may suggest that regardless of grade level or topic, the potential of learning from troubleshooting activi

关键词： erroneous examples learning from errors misconceptions peer assessment simple electric circuits troubleshooting activities worked examples

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Measuring the impact of productive failure on nursing students? learning in healthcare simulation: A quasi-experimental study

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NURSE EDUCATION TODAY 2021年 101卷 104871-104871页

作者： Palominos, Evelyn Levett-Jones, Tracy Power, Tamara Alcorn, Nadine Martinez-Maldonado, Roberto Univ Technol Sydney Fac Hlth 235 Jones St Ultimo NSW 2007 Australia Monash Univ Fac Informat Technol Clayton Vic Australia

Background: Previous research suggests that making errors in a non-threatening simulated environment can facilitate learning. Productive failure, which combines problem-solving tasks followed by instruction, enables students to learn from making mistakes. This teaching approach has demonstrated improved learning outcomes such as explanatory knowledge and transfer of knowledge compared to a direct instruction approach where students receive instruction prior to problem-solving tasks. However, no previous studies have examined the impact of productive failure on nursing students? learning in manikin-based simulation. Objective: To measure the impact of productive failure on nursing students? declarative knowledge, explanatory knowledge, and transfer of knowledge compared to a direct instruction approach in a paediatric closed head injury simulation. Methods: Second year undergraduate nursing students (n = 349) from one Australian university were invited to participate in the study. Consenting participants (n = 344) were randomised into two groups: productive failure and direct instruction. The intervention consisted of two paediatric closed head injury simulations separated by a simulation debrief. Knowledge tests were administered before and immediately after the simulation. Results: Data from 331 participants were analysed. The productive failure group outperformed the direct instruction group in the post-test (p < 0.001). learning gains for participants in the productive failure group were significantly higher than the direct instruction group for both explanatory knowledge (p < 0.001) and the ability to apply learning to solve novel clinical problems (p < 0.001). The difference in the median scores for declarative knowledge was not significant (p = 0.096). Conclusion: This study demonstrated that a productive failure simulation that leads learners to make mistakes before receiving instruction can facilitate deeper levels of explanatory knowledge and enable the tra

关键词： Direct instruction learning from errors learning outcomes Nursing education Productive failure Simulation-based learning

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Failure beliefs in school and beyond: from the perspective of social and emotional learning

Social and Emotional Learning: Research, Practice, and Polic...

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Social and Emotional learning: Research, Practice, and Policy 2025年 5卷

作者： Daisuke Akamatsu Claudia Gherghel Education Faculty Kyoto University of Education Japan Mori Arinori Institute for Higher Education and Global Mobility Hitotsubashi University Japan

Students inevitably experience failure in diverse contexts, both within and beyond the educational setting. As students have to learn how to cope with failure, cultivating resilience to failure is an important educational goal in the current society. This perspective paper undertakes a comprehensive review of studies centered around beliefs about academic failure, and highlights their importance in current educational settings, particularly in the context of social and emotional learning (SEL). After introducing the concept of failure beliefs within academic domains and providing an overview of prior research in this realm, we draw attention to the forthcoming horizons of research in failure belief studies. Future research is required (1) to position failure beliefs among various error-specific constructs in existing frameworks, (2) to understand how failure beliefs and other error-specific constructs relate to SEL, (3) to clarify the determinants of failure beliefs, (4) to examine the transfer and generalization of failure beliefs, and (5) to accumulate cross-cultural findings. Through these proposed directions, we underscore how failure beliefs stand to enrich SEL practices and policies.

关键词： learning from errors Failure belief Social and emotional learning Motivation Emotion

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Teaching the first and only logic control course with HOME I/O and Scratch 2.0 12th

Teaching the first and only logic control course with HOME I...

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12th IFAC Symposium on Advances in Control Education (ACE)

作者： Riera, B. Philippot, A. Annebicque, D. Univ Reims CReST UFR Sci Exactes & Nat BP 1039 F-51687 Reims France

This paper deals with teaching the first and only logic control course for 2nd year students (after the high school diploma) in computer science by using HOME I/O, the virtual house for control and STEM education and Scratch 2.0. HOME I/O is a fruitful collaboration between CReSTIC lab from the University of Reims Champagne-Ardenne and Real Games, a Portuguese company. In this paper, it is shown how HOME I/O combined with Scratch 2.0 has been used to present the main concepts of logic control. from a pedagogical point of view, an original approach based on learning from errors have been developed. After 2 years of experience, feedback from students and teachers have been very positive. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： logic control education learning from errors serious games

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"At least I know what's wrong." Preservice teachers' knowledge about dysfunctional instructional strategies: The important role of error-related emotional patterns

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learning AND INDIVIDUAL DIFFERENCES 2019年 70卷 190-200页

作者： Boehnke, Anja Thiel, Felicitas Free Univ Berlin Habelschwerdter Allee 45 D-14195 Berlin Germany

For preservice teachers, learning-oriented error-handling practices can play a central role in professional development. errors reveal areas preservice teachers have not yet mastered and can act as catalysts for informal learning processes. Yet for most people, errors are also linked to the experience of negative emotions. Research has found an array of associations between various error-related emotions and learning-oriented error-handling practices. Yet almost nothing is known about individual patterns of error-related emotions. In part 1 of our study, using a latent profile analysis of 208 preservice teachers, we identify four error-related emotional patterns (generally low emotions, anxiety-guilt profile, generally high emotions, anger-sadness profile). In part 2, using a latent moderated mediation model, we find that teachers' error-related emotional profiles predict their level of knowledge about dysfunctional instructional strategies, and that this association is mediated by the teacher's individual handling of his or her own instructional errors.

关键词： Teacher emotions Teacher knowledge learning from errors Latent profile analysis Moderated mediation

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A framework for negative knowledge to support hybrid geometric modeling education for product engineering

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JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING 2018年第1期5卷 80-93页

作者： Otto, Harald E. Mandorli, Ferruccio Polytech Univ Marche Via Brecce Bianche I-60131 Ancona Italy

Due to the full integration of CAD systems into modern product development and engineering, the competency to create usable geometric models has become an essential requirement for current CAD users. To avoid serious repercussions for future engineering labor, the focus of CAD education needs to be raised from the teaching of knowledge that is merely aimed at operating a system, to the development of basic strategic knowledge. from a pedagogical point of view, this situation represents a challenging task that requires new, innovative teaching methodologies. These new methodologies must facilitate the development of know-how and cognitive ability to organize domain knowledge within a holistic mental model allowing for accurate perception of the significance of circumstances and the possible consequences of actions. In this paper a new direction for CAD education is presented, based on the integration of traditional teaching methods with an educational approach based on negative knowledge. Analysis of first empirical results of this newly developed and implemented approach showed promising results. Improvements were observed in a better understanding of issues related to the usability of CAD models and an increased capability to recognize critical modeling situations and thus prevent the mistakes typically made by novices. Also, successful autonomous attempts could be observed of recovery from situations caused either by an accumulation of small mistakes or by severe modeling errors, which usually require remedial intervention by academic supervisors. (C) 2017 Society for Computational Design and Engineering. Publishing Services by Elsevier. This is an open access article under the CC BY-NC-ND license.

关键词： Normative geometric knowledge Strategic knowledge Negative expertise learning from errors

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Teaching the first and only logic control course with HOME I/O and Scratch 2.0

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IFAC-PapersOnLine 2019年第9期52卷 109-114页

作者： B. Riera A. Philippot D. Annebicque CReSTIC UFR Sciences Exactes et Naturelles University of Reims Champagne Ardenne Moulin de la Housse BP 1039 51687 Reims - France

This paper deals with teaching the first and only logic control course for 2 nd year students (after the high school diploma) in computer science by using HOME I/O, the virtual house for control and STEM education and Scratch 2.0. HOME I/O is a fruitful collaboration between CReSTIC lab from the University of Reims Champagne-Ardenne and Real Games, a Portuguese company. In this paper, it is shown how HOME I/O combined with Scratch 2.0 has been used to present the main concepts of logic control. from a pedagogical point of view, an original approach based on learning from errors have been developed. After 2 years of experience, feedback from students and teachers have been very positive.

关键词： logic control education learning from errors serious games

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Secondary School Students learning from Reflections on the Rationale Behind Self-Made errors: A Field Experiment

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JOURNAL OF EXPERIMENTAL EDUCATION 2016年第1期84卷 98-118页

作者： Heemsoth, Tim Heinze, Aiso Leibniz Inst Sci & Math Educ D-24118 Kiel Germany Univ Kiel Leibniz Inst Sci & Math Educ Math Educ Kiel Germany

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly assigned to one of two conditions: The students reflected on either the rationale behind their own errors or on the correct solution corresponding to their own errors. Students in the first condition group demonstrated a greater procedural knowledge at the posttest and at the follow-up test. Furthermore, at the follow-up test, these students demonstrated a higher conceptual knowledge. The implications for theory and school instruction are discussed.

关键词： knowledge learning from errors learning processes/strategies mathematics education secondary school

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